In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.